T(29,2)
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See other torus knots |
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Edit T(29,2) Further Notes and Views
Knot presentations
| Planar diagram presentation | X19,49,20,48 X49,21,50,20 X21,51,22,50 X51,23,52,22 X23,53,24,52 X53,25,54,24 X25,55,26,54 X55,27,56,26 X27,57,28,56 X57,29,58,28 X29,1,30,58 X1,31,2,30 X31,3,32,2 X3,33,4,32 X33,5,34,4 X5,35,6,34 X35,7,36,6 X7,37,8,36 X37,9,38,8 X9,39,10,38 X39,11,40,10 X11,41,12,40 X41,13,42,12 X13,43,14,42 X43,15,44,14 X15,45,16,44 X45,17,46,16 X17,47,18,46 X47,19,48,18 |
| Gauss code | -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21, 22, -23, 24, -25, 26, -27, 28, -29, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11 |
| Dowker-Thistlethwaite code | 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 2 4 6 8 10 12 14 16 18 20 22 24 26 28 |
| Braid presentation |
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Polynomial invariants
| Alexander polynomial | [math]\displaystyle{ t^{14}-t^{13}+t^{12}-t^{11}+t^{10}-t^9+t^8-t^7+t^6-t^5+t^4-t^3+t^2-t+1- t^{-1} + t^{-2} - t^{-3} + t^{-4} - t^{-5} + t^{-6} - t^{-7} + t^{-8} - t^{-9} + t^{-10} - t^{-11} + t^{-12} - t^{-13} + t^{-14} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{28}+27 z^{26}+325 z^{24}+2300 z^{22}+10626 z^{20}+33649 z^{18}+74613 z^{16}+116280 z^{14}+125970 z^{12}+92378 z^{10}+43758 z^8+12376 z^6+1820 z^4+105 z^2+1 }[/math] |
| 2nd Alexander ideal (db, data sources) | [math]\displaystyle{ \{1\} }[/math] |
| Determinant and Signature | { 29, 28 } |
| Jones polynomial | [math]\displaystyle{ -q^{43}+q^{42}-q^{41}+q^{40}-q^{39}+q^{38}-q^{37}+q^{36}-q^{35}+q^{34}-q^{33}+q^{32}-q^{31}+q^{30}-q^{29}+q^{28}-q^{27}+q^{26}-q^{25}+q^{24}-q^{23}+q^{22}-q^{21}+q^{20}-q^{19}+q^{18}-q^{17}+q^{16}+q^{14} }[/math] |
| HOMFLY-PT polynomial (db, data sources) | [math]\displaystyle{ z^{28}a^{-28}-28z^{26}a^{-28}-z^{26}a^{-30}+351z^{24}a^{-28}+26z^{24}a^{-30}-2600z^{22}a^{-28}-300z^{22}a^{-30}+12650z^{20}a^{-28}+2024z^{20}a^{-30}-42504z^{18}a^{-28}-8855z^{18}a^{-30}+100947z^{16}a^{-28}+26334z^{16}a^{-30}-170544z^{14}a^{-28}-54264z^{14}a^{-30}+203490z^{12}a^{-28}+77520z^{12}a^{-30}-167960z^{10}a^{-28}-75582z^{10}a^{-30}+92378z^8a^{-28}+48620z^8a^{-30}-31824z^6a^{-28}-19448z^6a^{-30}+6188z^4a^{-28}+4368z^4a^{-30}-560z^2a^{-28}-455z^2a^{-30}+15a^{-28}+14a^{-30} }[/math] |
| Kauffman polynomial (db, data sources) | [math]\displaystyle{ z^{28}a^{-28}+z^{28}a^{-30}+z^{27}a^{-29}+z^{27}a^{-31}-28z^{26}a^{-28}-27z^{26}a^{-30}+z^{26}a^{-32}-26z^{25}a^{-29}-25z^{25}a^{-31}+z^{25}a^{-33}+351z^{24}a^{-28}+326z^{24}a^{-30}-24z^{24}a^{-32}+z^{24}a^{-34}+300z^{23}a^{-29}+276z^{23}a^{-31}-23z^{23}a^{-33}+z^{23}a^{-35}-2600z^{22}a^{-28}-2324z^{22}a^{-30}+253z^{22}a^{-32}-22z^{22}a^{-34}+z^{22}a^{-36}-2024z^{21}a^{-29}-1771z^{21}a^{-31}+231z^{21}a^{-33}-21z^{21}a^{-35}+z^{21}a^{-37}+12650z^{20}a^{-28}+10879z^{20}a^{-30}-1540z^{20}a^{-32}+210z^{20}a^{-34}-20z^{20}a^{-36}+z^{20}a^{-38}+8855z^{19}a^{-29}+7315z^{19}a^{-31}-1330z^{19}a^{-33}+190z^{19}a^{-35}-19z^{19}a^{-37}+z^{19}a^{-39}-42504z^{18}a^{-28}-35189z^{18}a^{-30}+5985z^{18}a^{-32}-1140z^{18}a^{-34}+171z^{18}a^{-36}-18z^{18}a^{-38}+z^{18}a^{-40}-26334z^{17}a^{-29}-20349z^{17}a^{-31}+4845z^{17}a^{-33}-969z^{17}a^{-35}+153z^{17}a^{-37}-17z^{17}a^{-39}+z^{17}a^{-41}+100947z^{16}a^{-28}+80598z^{16}a^{-30}-15504z^{16}a^{-32}+3876z^{16}a^{-34}-816z^{16}a^{-36}+136z^{16}a^{-38}-16z^{16}a^{-40}+z^{16}a^{-42}+54264z^{15}a^{-29}+38760z^{15}a^{-31}-11628z^{15}a^{-33}+3060z^{15}a^{-35}-680z^{15}a^{-37}+120z^{15}a^{-39}-15z^{15}a^{-41}+z^{15}a^{-43}-170544z^{14}a^{-28}-131784z^{14}a^{-30}+27132z^{14}a^{-32}-8568z^{14}a^{-34}+2380z^{14}a^{-36}-560z^{14}a^{-38}+105z^{14}a^{-40}-14z^{14}a^{-42}+z^{14}a^{-44}-77520z^{13}a^{-29}-50388z^{13}a^{-31}+18564z^{13}a^{-33}-6188z^{13}a^{-35}+1820z^{13}a^{-37}-455z^{13}a^{-39}+91z^{13}a^{-41}-13z^{13}a^{-43}+z^{13}a^{-45}+203490z^{12}a^{-28}+153102z^{12}a^{-30}-31824z^{12}a^{-32}+12376z^{12}a^{-34}-4368z^{12}a^{-36}+1365z^{12}a^{-38}-364z^{12}a^{-40}+78z^{12}a^{-42}-12z^{12}a^{-44}+z^{12}a^{-46}+75582z^{11}a^{-29}+43758z^{11}a^{-31}-19448z^{11}a^{-33}+8008z^{11}a^{-35}-3003z^{11}a^{-37}+1001z^{11}a^{-39}-286z^{11}a^{-41}+66z^{11}a^{-43}-11z^{11}a^{-45}+z^{11}a^{-47}-167960z^{10}a^{-28}-124202z^{10}a^{-30}+24310z^{10}a^{-32}-11440z^{10}a^{-34}+5005z^{10}a^{-36}-2002z^{10}a^{-38}+715z^{10}a^{-40}-220z^{10}a^{-42}+55z^{10}a^{-44}-10z^{10}a^{-46}+z^{10}a^{-48}-48620z^9a^{-29}-24310z^9a^{-31}+12870z^9a^{-33}-6435z^9a^{-35}+3003z^9a^{-37}-1287z^9a^{-39}+495z^9a^{-41}-165z^9a^{-43}+45z^9a^{-45}-9z^9a^{-47}+z^9a^{-49}+92378z^8a^{-28}+68068z^8a^{-30}-11440z^8a^{-32}+6435z^8a^{-34}-3432z^8a^{-36}+1716z^8a^{-38}-792z^8a^{-40}+330z^8a^{-42}-120z^8a^{-44}+36z^8a^{-46}-8z^8a^{-48}+z^8a^{-50}+19448z^7a^{-29}+8008z^7a^{-31}-5005z^7a^{-33}+3003z^7a^{-35}-1716z^7a^{-37}+924z^7a^{-39}-462z^7a^{-41}+210z^7a^{-43}-84z^7a^{-45}+28z^7a^{-47}-7z^7a^{-49}+z^7a^{-51}-31824z^6a^{-28}-23816z^6a^{-30}+3003z^6a^{-32}-2002z^6a^{-34}+1287z^6a^{-36}-792z^6a^{-38}+462z^6a^{-40}-252z^6a^{-42}+126z^6a^{-44}-56z^6a^{-46}+21z^6a^{-48}-6z^6a^{-50}+z^6a^{-52}-4368z^5a^{-29}-1365z^5a^{-31}+1001z^5a^{-33}-715z^5a^{-35}+495z^5a^{-37}-330z^5a^{-39}+210z^5a^{-41}-126z^5a^{-43}+70z^5a^{-45}-35z^5a^{-47}+15z^5a^{-49}-5z^5a^{-51}+z^5a^{-53}+6188z^4a^{-28}+4823z^4a^{-30}-364z^4a^{-32}+286z^4a^{-34}-220z^4a^{-36}+165z^4a^{-38}-120z^4a^{-40}+84z^4a^{-42}-56z^4a^{-44}+35z^4a^{-46}-20z^4a^{-48}+10z^4a^{-50}-4z^4a^{-52}+z^4a^{-54}+455z^3a^{-29}+91z^3a^{-31}-78z^3a^{-33}+66z^3a^{-35}-55z^3a^{-37}+45z^3a^{-39}-36z^3a^{-41}+28z^3a^{-43}-21z^3a^{-45}+15z^3a^{-47}-10z^3a^{-49}+6z^3a^{-51}-3z^3a^{-53}+z^3a^{-55}-560z^2a^{-28}-469z^2a^{-30}+13z^2a^{-32}-12z^2a^{-34}+11z^2a^{-36}-10z^2a^{-38}+9z^2a^{-40}-8z^2a^{-42}+7z^2a^{-44}-6z^2a^{-46}+5z^2a^{-48}-4z^2a^{-50}+3z^2a^{-52}-2z^2a^{-54}+z^2a^{-56}-14za^{-29}-za^{-31}+za^{-33}-za^{-35}+za^{-37}-za^{-39}+za^{-41}-za^{-43}+za^{-45}-za^{-47}+za^{-49}-za^{-51}+za^{-53}-za^{-55}+za^{-57}+15a^{-28}+14a^{-30} }[/math] |
| The A2 invariant | Data:T(29,2)/QuantumInvariant/A2/1,0 |
| The G2 invariant | Data:T(29,2)/QuantumInvariant/G2/1,0 |
Further Quantum Invariants
Computer Talk
The above data is available with the Mathematica package
KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
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In[3]:=
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K = Knot["T(29,2)"];
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In[4]:=
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Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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[math]\displaystyle{ t^{14}-t^{13}+t^{12}-t^{11}+t^{10}-t^9+t^8-t^7+t^6-t^5+t^4-t^3+t^2-t+1- t^{-1} + t^{-2} - t^{-3} + t^{-4} - t^{-5} + t^{-6} - t^{-7} + t^{-8} - t^{-9} + t^{-10} - t^{-11} + t^{-12} - t^{-13} + t^{-14} }[/math] |
In[5]:=
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Conway[K][z]
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Out[5]=
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[math]\displaystyle{ z^{28}+27 z^{26}+325 z^{24}+2300 z^{22}+10626 z^{20}+33649 z^{18}+74613 z^{16}+116280 z^{14}+125970 z^{12}+92378 z^{10}+43758 z^8+12376 z^6+1820 z^4+105 z^2+1 }[/math] |
In[6]:=
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Alexander[K, 2][t]
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KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
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Out[6]=
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[math]\displaystyle{ \{1\} }[/math] |
In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ 29, 28 } |
In[8]:=
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Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
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[math]\displaystyle{ -q^{43}+q^{42}-q^{41}+q^{40}-q^{39}+q^{38}-q^{37}+q^{36}-q^{35}+q^{34}-q^{33}+q^{32}-q^{31}+q^{30}-q^{29}+q^{28}-q^{27}+q^{26}-q^{25}+q^{24}-q^{23}+q^{22}-q^{21}+q^{20}-q^{19}+q^{18}-q^{17}+q^{16}+q^{14} }[/math] |
In[9]:=
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HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
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Out[9]=
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[math]\displaystyle{ z^{28}a^{-28}-28z^{26}a^{-28}-z^{26}a^{-30}+351z^{24}a^{-28}+26z^{24}a^{-30}-2600z^{22}a^{-28}-300z^{22}a^{-30}+12650z^{20}a^{-28}+2024z^{20}a^{-30}-42504z^{18}a^{-28}-8855z^{18}a^{-30}+100947z^{16}a^{-28}+26334z^{16}a^{-30}-170544z^{14}a^{-28}-54264z^{14}a^{-30}+203490z^{12}a^{-28}+77520z^{12}a^{-30}-167960z^{10}a^{-28}-75582z^{10}a^{-30}+92378z^8a^{-28}+48620z^8a^{-30}-31824z^6a^{-28}-19448z^6a^{-30}+6188z^4a^{-28}+4368z^4a^{-30}-560z^2a^{-28}-455z^2a^{-30}+15a^{-28}+14a^{-30} }[/math] |
In[10]:=
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Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
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[math]\displaystyle{ z^{28}a^{-28}+z^{28}a^{-30}+z^{27}a^{-29}+z^{27}a^{-31}-28z^{26}a^{-28}-27z^{26}a^{-30}+z^{26}a^{-32}-26z^{25}a^{-29}-25z^{25}a^{-31}+z^{25}a^{-33}+351z^{24}a^{-28}+326z^{24}a^{-30}-24z^{24}a^{-32}+z^{24}a^{-34}+300z^{23}a^{-29}+276z^{23}a^{-31}-23z^{23}a^{-33}+z^{23}a^{-35}-2600z^{22}a^{-28}-2324z^{22}a^{-30}+253z^{22}a^{-32}-22z^{22}a^{-34}+z^{22}a^{-36}-2024z^{21}a^{-29}-1771z^{21}a^{-31}+231z^{21}a^{-33}-21z^{21}a^{-35}+z^{21}a^{-37}+12650z^{20}a^{-28}+10879z^{20}a^{-30}-1540z^{20}a^{-32}+210z^{20}a^{-34}-20z^{20}a^{-36}+z^{20}a^{-38}+8855z^{19}a^{-29}+7315z^{19}a^{-31}-1330z^{19}a^{-33}+190z^{19}a^{-35}-19z^{19}a^{-37}+z^{19}a^{-39}-42504z^{18}a^{-28}-35189z^{18}a^{-30}+5985z^{18}a^{-32}-1140z^{18}a^{-34}+171z^{18}a^{-36}-18z^{18}a^{-38}+z^{18}a^{-40}-26334z^{17}a^{-29}-20349z^{17}a^{-31}+4845z^{17}a^{-33}-969z^{17}a^{-35}+153z^{17}a^{-37}-17z^{17}a^{-39}+z^{17}a^{-41}+100947z^{16}a^{-28}+80598z^{16}a^{-30}-15504z^{16}a^{-32}+3876z^{16}a^{-34}-816z^{16}a^{-36}+136z^{16}a^{-38}-16z^{16}a^{-40}+z^{16}a^{-42}+54264z^{15}a^{-29}+38760z^{15}a^{-31}-11628z^{15}a^{-33}+3060z^{15}a^{-35}-680z^{15}a^{-37}+120z^{15}a^{-39}-15z^{15}a^{-41}+z^{15}a^{-43}-170544z^{14}a^{-28}-131784z^{14}a^{-30}+27132z^{14}a^{-32}-8568z^{14}a^{-34}+2380z^{14}a^{-36}-560z^{14}a^{-38}+105z^{14}a^{-40}-14z^{14}a^{-42}+z^{14}a^{-44}-77520z^{13}a^{-29}-50388z^{13}a^{-31}+18564z^{13}a^{-33}-6188z^{13}a^{-35}+1820z^{13}a^{-37}-455z^{13}a^{-39}+91z^{13}a^{-41}-13z^{13}a^{-43}+z^{13}a^{-45}+203490z^{12}a^{-28}+153102z^{12}a^{-30}-31824z^{12}a^{-32}+12376z^{12}a^{-34}-4368z^{12}a^{-36}+1365z^{12}a^{-38}-364z^{12}a^{-40}+78z^{12}a^{-42}-12z^{12}a^{-44}+z^{12}a^{-46}+75582z^{11}a^{-29}+43758z^{11}a^{-31}-19448z^{11}a^{-33}+8008z^{11}a^{-35}-3003z^{11}a^{-37}+1001z^{11}a^{-39}-286z^{11}a^{-41}+66z^{11}a^{-43}-11z^{11}a^{-45}+z^{11}a^{-47}-167960z^{10}a^{-28}-124202z^{10}a^{-30}+24310z^{10}a^{-32}-11440z^{10}a^{-34}+5005z^{10}a^{-36}-2002z^{10}a^{-38}+715z^{10}a^{-40}-220z^{10}a^{-42}+55z^{10}a^{-44}-10z^{10}a^{-46}+z^{10}a^{-48}-48620z^9a^{-29}-24310z^9a^{-31}+12870z^9a^{-33}-6435z^9a^{-35}+3003z^9a^{-37}-1287z^9a^{-39}+495z^9a^{-41}-165z^9a^{-43}+45z^9a^{-45}-9z^9a^{-47}+z^9a^{-49}+92378z^8a^{-28}+68068z^8a^{-30}-11440z^8a^{-32}+6435z^8a^{-34}-3432z^8a^{-36}+1716z^8a^{-38}-792z^8a^{-40}+330z^8a^{-42}-120z^8a^{-44}+36z^8a^{-46}-8z^8a^{-48}+z^8a^{-50}+19448z^7a^{-29}+8008z^7a^{-31}-5005z^7a^{-33}+3003z^7a^{-35}-1716z^7a^{-37}+924z^7a^{-39}-462z^7a^{-41}+210z^7a^{-43}-84z^7a^{-45}+28z^7a^{-47}-7z^7a^{-49}+z^7a^{-51}-31824z^6a^{-28}-23816z^6a^{-30}+3003z^6a^{-32}-2002z^6a^{-34}+1287z^6a^{-36}-792z^6a^{-38}+462z^6a^{-40}-252z^6a^{-42}+126z^6a^{-44}-56z^6a^{-46}+21z^6a^{-48}-6z^6a^{-50}+z^6a^{-52}-4368z^5a^{-29}-1365z^5a^{-31}+1001z^5a^{-33}-715z^5a^{-35}+495z^5a^{-37}-330z^5a^{-39}+210z^5a^{-41}-126z^5a^{-43}+70z^5a^{-45}-35z^5a^{-47}+15z^5a^{-49}-5z^5a^{-51}+z^5a^{-53}+6188z^4a^{-28}+4823z^4a^{-30}-364z^4a^{-32}+286z^4a^{-34}-220z^4a^{-36}+165z^4a^{-38}-120z^4a^{-40}+84z^4a^{-42}-56z^4a^{-44}+35z^4a^{-46}-20z^4a^{-48}+10z^4a^{-50}-4z^4a^{-52}+z^4a^{-54}+455z^3a^{-29}+91z^3a^{-31}-78z^3a^{-33}+66z^3a^{-35}-55z^3a^{-37}+45z^3a^{-39}-36z^3a^{-41}+28z^3a^{-43}-21z^3a^{-45}+15z^3a^{-47}-10z^3a^{-49}+6z^3a^{-51}-3z^3a^{-53}+z^3a^{-55}-560z^2a^{-28}-469z^2a^{-30}+13z^2a^{-32}-12z^2a^{-34}+11z^2a^{-36}-10z^2a^{-38}+9z^2a^{-40}-8z^2a^{-42}+7z^2a^{-44}-6z^2a^{-46}+5z^2a^{-48}-4z^2a^{-50}+3z^2a^{-52}-2z^2a^{-54}+z^2a^{-56}-14za^{-29}-za^{-31}+za^{-33}-za^{-35}+za^{-37}-za^{-39}+za^{-41}-za^{-43}+za^{-45}-za^{-47}+za^{-49}-za^{-51}+za^{-53}-za^{-55}+za^{-57}+15a^{-28}+14a^{-30} }[/math] |
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, [math]\displaystyle{ q\leftrightarrow q^{-1} }[/math]): {}
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["T(29,2)"];
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In[4]:=
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{A = Alexander[K][t], J = Jones[K][q]}
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[4]=
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{ [math]\displaystyle{ t^{14}-t^{13}+t^{12}-t^{11}+t^{10}-t^9+t^8-t^7+t^6-t^5+t^4-t^3+t^2-t+1- t^{-1} + t^{-2} - t^{-3} + t^{-4} - t^{-5} + t^{-6} - t^{-7} + t^{-8} - t^{-9} + t^{-10} - t^{-11} + t^{-12} - t^{-13} + t^{-14} }[/math], [math]\displaystyle{ -q^{43}+q^{42}-q^{41}+q^{40}-q^{39}+q^{38}-q^{37}+q^{36}-q^{35}+q^{34}-q^{33}+q^{32}-q^{31}+q^{30}-q^{29}+q^{28}-q^{27}+q^{26}-q^{25}+q^{24}-q^{23}+q^{22}-q^{21}+q^{20}-q^{19}+q^{18}-q^{17}+q^{16}+q^{14} }[/math] } |
In[5]:=
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DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
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KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
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KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
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Out[5]=
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{} |
In[6]:=
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DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
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KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
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Out[6]=
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{} |
Vassiliev invariants
| V2 and V3: | (105, 1015) |
| V2,1 through V6,9: |
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V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
| The coefficients of the monomials [math]\displaystyle{ t^rq^j }[/math] are shown, along with their alternating sums [math]\displaystyle{ \chi }[/math] (fixed [math]\displaystyle{ j }[/math], alternation over [math]\displaystyle{ r }[/math]). The squares with yellow highlighting are those on the "critical diagonals", where [math]\displaystyle{ j-2r=s+1 }[/math] or [math]\displaystyle{ j-2r=s-1 }[/math], where [math]\displaystyle{ s= }[/math]28 is the signature of T(29,2). Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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| Integral Khovanov Homology
(db, data source) |
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Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Torus Knot Page master template (intermediate). See/edit the Torus Knot_Splice_Base (expert). Back to the top. |
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